相关论文: A numerical approach to large deviations in contin…

Switching dynamical systems provide a powerful, interpretable modeling framework for inference in time-series data in, e.g., the natural sciences or engineering applications. Since many areas, such as biology or discrete-event systems, are…

We discuss the Giardin\`a-Kurchan-Peliti population dynamics method for evaluating large deviations of time averaged quantities in Markov processes [Phys. Rev. Lett. \textbf{96}, 120603 (2006)]. This method exhibits systematic errors which…

In many change point problems it is reasonable to assume that compared to a benchmark at a given time point $t_0$ the properties of the observed stochastic process change gradually over time for $t >t_0$. Often, these gradual changes are…

We describe a simple form of importance sampling designed to bound and compute large-deviation rate functions for time-extensive dynamical observables in continuous-time Markov chains. We start with a model, defined by a set of rates, and a…

Physical systems can often be described via a continuous-time dynamical system. In practice, the true system is often unknown and has to be learned from measurement data. Since data is typically collected in discrete time, e.g. by sensors,…

The theory of large deviations is concerned with the exponential decay of probabilities of large fluctuations in random systems. These probabilities are important in many fields of study, including statistics, finance, and engineering, as…

In this paper we provide a rigorous mathematical foundation for continuous approximations of a class of systems with piece-wise continuous functions. By using techniques from the theory of differential inclusions, the underlying piece-wise…

We develop the connection between large deviation theory and more applied approaches to stochastic hybrid systems by highlighting a common underlying Hamiltonian structure. A stochastic hybrid system involves the coupling between a…

In this work, we propose a numerical approach for simulations of large deformations of interfaces in a level set framework. To obtain a fast and viable numerical solution in both time and space, temporal discretization is based on the…

We consider a dynamic method, based on synchronization and adaptive control, to estimate unknown parameters of a nonlinear dynamical system from a given scalar chaotic time series. We present an important extension of the method when time…

We study the performance of a stochastic algorithm based on the power method that adaptively learns the large deviation functions characterizing the fluctuations of additive functionals of Markov processes, used in physics to model…

Large deviation functions contain information on the stability and response of systems driven into nonequilibrium steady states, and in such a way are similar to free energies for systems at equilibrium. As with equilibrium free energies,…

We propose a computational method for large deviation statistics of time-averaged quantities in general Markov processes. In our proposed method, we repeat a response measurement against external forces, where the forces are determined by…

In this work we consider time series with a finite number of discrete point changes. We assume that the data in each segment follows a different probability density functions (pdf). We focus on the case where the data in all segments are…

We investigate the Large Deviation behavior in small time of continuous Gaussian processes. We introduce a general procedure allowing to derive Large Deviation Principles in small time starting from the well understood context of Large…

We consider a two-dimensional Hamiltonian system perturbed by a small diffusion term, whose coefficient is state-dependent and non-degenerate. As a result, the process consists of the fast motion along the level curves and slow motion…

We describe a framework to significantly reduce the computational effort to evaluate large deviation functions of time integrated observables within nonequilibrium steady states. We do this by incorporating an auxiliary dynamics into…

Time-irreversible stochastic processes are frequently used in natural sciences to explain non-equilibrium phenomena and to design efficient stochastic algorithms. Our main goal in this thesis is to analyse their dynamics by means of large…

These notes give a summary of techniques used in large deviation theory to study the fluctuations of time-additive quantities, called dynamical observables, defined in the context of Langevin-type equations, which model equilibrium and…

An approach is presented for making predictions about functional time series. The method is applied to data coming from periodically correlated processes and electricity demand, obtaining accurate point forecasts and narrow prediction bands…